Question #588d8
1 Answer
May 22, 2017
Use the identities:
#sin(x+y)=sin(x)cos(y)+cos(x)sin(y)#
#cos(x-y)=cos(x)cos(y)+sin(x)sin(y)#
#sin^2x+cos^2x=1#
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We will start with the LHS:
#sin(x+y)cos(x-y)#
#(sinxcosy+cosxsiny)(cosxcosy+sinxsiny)#
Now use the FOIL method (from the good ol' days back in Algebra 1)
#sinxcosxcos^2y+sin^2xsinycosy+cos^2xsinycosy+sinxcosxsin^2y#
#(sin^2y+cos^2y)(sinxcosx)+(sin^2x+cos^2x)(sinycosy)#
Now use the third identity listed above.
#sinxcosx+sinycosy#
In fact,